Imagine the most basic monster you can, a floating blob with teeth. The blob monster.
We could represent a low level blob monster with a single dice, a d6, sat on the table, on the value 6. The blob monster has 6HP, it adds 6 to attacks rolls, and when it hits, it does 6 Damage. Simple.
When Belinda the Fighter takes a swing at it with her axe, and does 4 Damage to the blob, she takes a good chunk out of it, and it’s looking battered. I turn the dice around, and it’s now sat on a 2. 2 HP left, adding 2 to attack rolls and doing 2 damage when it hits. By injuring the blob, it’s now less effective in combat, as its weakened.
Want a tougher blob? Make it a d8, or a d10. What about a huge blob monster as a d20! The magic user might want to throw a fireball at that one first, before Belinda wades into the fray.
We can go further. What if it’s a more complex monster, with multiple limbs or ways of attacking? Like a bat:
So the Bat has a mouth full of sharp teeth that deal a d6 damage, and a couple of weedy wings just keeping its pudgy frame airborne. Its guna bite the characters if its given the option. But what if Belinda takes another swing of her axe to the beast, dealing 3 Damage to the poor things face? Now, maybe it changes tactics. With a wounded jaw, it starts clawing at its opponents with its d4 wings.
Perhaps Jeffry see’s an opportunity to incapacitate their enemy, and shoot its wings off. Do 4 damage to a wing, and it’s been chopped off. A Wingless bat hobbling across the floor to bite you isn’t as much of a threat anymore.
I think you get the basic idea. Lets run with it:
With larger monsters, giving their main bulk a dice gives them more survivability. Perhaps this is what gets hit by AOE attacks, or missed called shots, etc. Maybe you just remove damage from that first? It's up to you. I think context plays a bit role here.
The d8 is the Dire Rat's bite damage, the d6 would be it's claws and d4 it's tail should it have to resort to it.
The main threat of a Balilisk is it's head and it's gaze attacks. Giving the head high hit points and damage represents it's bite attack and armoured scales. You could use d4s for its eyes. The tail of d6s can keep being chopped off bit by bit, but it's always doing 6 damage.
Dragons are big and scary so giving it lots of bits to lop off is fun. The d10 represents the head for bite attacks or perhaps a breath weapon. The d4s are wings, the d8s it's legs for claw attacks and the d6s are it's tail. Like the Ogre, giving it some bulk can help make it feel more like a big beasty.
This is the monster that first came to mind when I thought of this. With each head being a d6, you can easily replace every one they chop off with another two. Plus is presents an interesting option; injure all the heads until they do very little damage, without chopping them off, and they don't grow back.Then destroy the body.
What is a beholder if not a blob monster with lots of weedy eye stalks?
In reality I would run NPCs as characters, not like a monster, but the point still stands that you could use this method to model any humanoid.
Taking this and running with it, we can come up with all sorts of monsters. Tune the monster difficulty by increasing the number of dice or their size. Perhaps some of the dice start at a lower value, but require the full amount of damage to destroy.
This makes players think about monsters more in terms of their physicality, and provide opportunities for player creativity and choice. It also does away with a bunch of bookkeeping on the GM’s side of things, and saves on paper which I inevitably scrawl all over when tracking different pools of hit points during a fight.
I generally think this will only work for 1-3 monsters, before it gets unwieldy, but for a boss fight it would work wonderfully. A bunch of mooks could be just a single dice, so if you have a load of d6s that would work.
If you try it out, let me know how it goes!